Quasidifferential Calculus (Translations Series in Mathematics and Engineering)

TABLE OF CONTENTS......Page 8 PREFACE......Page 10 1 PRELIMINARIES......Page 14 2 ELEMENTS OF THE THEORYOF MULTIVALUED MAPPINGS......Page 19 3 DIRECTIONAL DERIVATIVES......Page 32 4 CONVEX FUNCTIONS......Page 50 5 SUBLINEAR FUNCTIONS......Page 59 6 THE SPACE OF CONVEX SETS......Page 78 7 UPPER -SEMICONTINUO USLYDIRECTIONALLY DIFFERENTIABLEFUNCTIONS......Page 91 8 THE CLARKS DERIVATIVES......Page 104 9 UPPER CONVEX ANDLOWER CONCAVE APPROXIMATIONS......Page 117 10 Q UASIDIFFERENTIABLE FUNCTIONS......Page 125 11 EXAMPLES......Page 135 12 QUASIDIFFERENTL4BILITY OF A COMPOSITION......Page 141 13 A RELATION BETWEENTHE CLARKE SUBDIFFERENTIALAND THE QUASIDIFFERENTIALS......Page 156 14 IMPLICIT AND INVERSEFUNCTION THEOREMS......Page 168 15 CONES OF ADMISSIBLE DIRECTIONSAND A NONDEGENERACY CONDITION......Page 189 16 NECESSARY AND SUFFICIENTCONDITIONS FOR AN EXTREMUM......Page 201 17 RATE AND DIRECTIONS OFSTEEPEST DESCENT AND ASCENT......Page 216 18 SADDLE POINTS OFQ UASIDIFFERENTIABLE FUNCTIONS......Page 242 19 STAR-SHAPED SETS AND THEIR APPLICATIONSIN NONSMOOTH OPTIMIZATION......Page 249 20 APPROXIMATE Q UASIDIFFERENTIABILITY......Page 267 BIBLIOGRAPHIC NOTES......Page 278 REFERENCES......Page 282 INDEX......Page 296 TRANSLITERATION TABLE......Page 302